Magnetic Solitons Research Articles

The solitary wave solutions of the stochastic Heisenberg ferromagnetic spin chain equation using two different analytical methods

Here, we consider the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which is forced by the multiplicative Brownian motion in the Stratonovich sense. We utilize the (G′/G)-expansion method and the mapping method to attain the analytical solutions of the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic chain equation. Various types of analytical stochastic solutions, such as the hyperbolic, elliptic, and trigonometric functions, have been obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because the magnetic soliton has been categorized as one of the interesting groups of nonlinear excitations representing spin dynamics in the semiclassical continuum Heisenberg systems. Moreover, we employ MATLAB tools to plot 3D and 2D graphs for some obtained solutions to address the influence of Brownian motion on these solutions.

A positive energy theorem for AdS solitons

The uncharged AdS4 soliton has been recently shown to be continuously connected to a magnetic, supersymmetric AdS4 soliton within N=8 gauged supergravity. By constructing the asymptotic superalgebra, we establish a positive energy theorem for the magnetic AdS4 solitons admitting well-defined asymptotic Killing spinors, antiperiodic on a contractible S1. We show that there exists only one discrete solution endowed with these boundary conditions satisfying the bound, the latter being saturated by the null energy supersymmetric configuration. Despite having negative energy, the uncharged AdS4 soliton does not contradict the positive energy theorem, as it does not admit well-defined asymptotic Killing spinors.

Fe Doping-Induced Magnetic Solitons in CrNb3S6

Fe Doping-Induced Magnetic Solitons in CrNb3S6

Surface barrier effect as evidence of chiral soliton lattice formation in chiral dichalcogenide CrTa3S6 crystals

The formation of chiral magnetic soliton lattice (CSL) is investigated in monoaxial chiral dichalcogenide CrTa3S6 crystals in terms of a surface barrier, which prevents the penetration of chiral solitons into the system and is an intrinsic origin of hysteresis for the continuous phase transition of nucleation-type, as discussed in the system of quantized vortices in type-II superconductors. The magnetoresistance (MR) was examined with microfabricated platelet samples in different dimensions with regard to the c-axis direction of the crystal. The CSL formation was confirmed by the discrete MR changes, reflecting the number of chiral solitons, as well as by the presence of a surface barrier, recognized as a fixed ratio of critical magnetic fields during the hysteresis field cycle. We also argue the influence of the surface barrier in bulk CrTa3S6 crystals.

Stability and asymptotic interactions of chiral magnetic skyrmions in a tilted magnetic field

Using a general framework, interaction potentials between chiral magnetic solitons in a planar system with a tilted external magnetic field are calculated analytically in the limit of large separation. The results are compared to previous numerical results for solitons with topological charge \pm 1±1. A key feature of the calculation is the interpretation of Dzyaloshinskii-Moriya interaction (DMI) as a background SO(3)SO(3) gauge field. In a tilted field, this leads to a U(1)U(1)-gauged version of the usual equation for spin excitations, leading to a distinctive oscillating interaction profile. We also obtain predictions for skyrmion stability in a tilted field which closely match numerical observations.

Emergent magnetic field and vector potential of the toroidal magnetic hopfions

Magnetic hopfions are localized magnetic solitons with non-zero 3D topological charge (Hopf index). Here I present an analytical calculation of the toroidal magnetic hopfion vector potential, emergent magnetic field, the Hopf index, and the magnetization configuration. The calculation method is based on the concept of the spinor representation of the Hopf mapping. The hopfions with arbitrary values of the azimuthal and poloidal vorticities are considered. The special role of the toroidal coordinates and their connection with the emergent vector potential gauge are demonstrated. The hopfion magnetization field is found explicitly for the arbitrary Hopf indices. It is shown that the Hopf charge density can be represented as a Jacobian of the transformation from the toroidal to the cylindrical coordinates.

Chirality reversal of magnetic solitons in chiral Cr1/3TaS2

Ferromagnetism in two-dimensional (2D) materials provides an ideal platform to study emergent electromagnetic phenomena in low dimensions for future spintronics. In magnetic-element intercalated transition metal dichalcogenides, topologically nontrivial spin textures, such as chiral helimagnetic spin states and chiral soliton lattices, are realized due to the chiral lattice distortions induced by intercalated magnetic ions. Consequently, the magnetic chirality is predictably determined by the sign of antisymmetric exchange interaction (or Dzyaloshinskii–Moriya interaction, DMI) vector that is coupled to the underlying crystal chirality. Here, using cryogenic Lorentz phase microscopy, we directly observed the chirality reversal behavior of the chiral soliton lattices in Cr1/3TaS2 across the structural defects. We show that a partial 1 T stacking in 2H-TaS2 locally reduces DMI, leading to magnetic chirality reversal with direct atomic resolution imaging. Our experimental results show that manipulation of stacking sequence provides a viable way to control the chirality of topologically nontrivial soliton lattices in 2D magnets.

Harmonic oscillations of point soliton (Bloch point) in cylindrical ferromagnetic nanowire

Harmonic oscillations of a point magnetic soliton (Bloch point) located in a domain wall (DW) of a cylindrical ferromagnetic nanowire along the spatial directions of a primitive vortex cell formed by the magnetization vectors at the boundary between the core and the transition zone of the soliton are considered. The possibility of experimental implementation of Bloch point resonant oscillations excited by external alternating magnetic field is shown. In the case of weak attenuation, the maximum values of the resonant frequencies of Bloch points in iron and nickel nanowires are determined, which are 10 and 3 GHz, respectively. These results can be applied in the modern nanotechnologies based on the use of the magnetic properties of ferromagnetic nanowires whose DWs contain Bloch points.

The Progress on Magnetic Material Thin Films Prepared Using Polymer-Assisted Deposition.

Polymer-assisted deposition (PAD) has been widely used in the preparation of high-quality oxides and sulfides for basic research and applications. Specifically, diverse PAD-prepared magnetic material thin films such as ZnO, Ga2O3, SrRuO3, LaCoO3, LaMnO3, Y3Fe5O12, MoS2, MoSe2, and ReS2 thin films have been grown, in which thickness-dependent, strain-modulated, doping-mediated, and/or morphology-dependent room-temperature ferromagnetism (RTFM) have been explored. Inspired by the discovery of intrinsic low-temperature FM in two-dimensional (2D) systems prepared using mechanical exfoliation, the search for more convenient methods to prepare 2D ferromagnetic materials with high-temperature FM has seen explosive growth, but with little success. Fortunately, the very recent synthesis of 2D NiO by PAD has shed light on this challenge. Based on these abovementioned developments, the difficulties of PAD when preparing a-few-nanometer single-crystalline materials and the opportunities in PAD for novel materials such as chiral magnetic soliton material Cr1/3NbS2 are discussed.

Propagations of multiple solitons in a deformed ferrite

In this work, we investigate the magnetic soliton profile and propagation properties of ultrashort waves in one-dimensional deformed ferrite. A generalized variable-coefficient (1+1)-dimensional ultrashort wave model is obtained by employing the multi-scale expansion method and short-wave approximation. Using numerical simulations, we examine the impact of multiple inhomogeneities on the transmission of magnetic solitons, which arise from local and periodic deformations. Our results indicate that the localized inhomogeneity alter the velocity of magnetic solitons, allowing for the manipulation of their acceleration or deceleration. Periodic type deformation inhomogeneities, on the other hand, provide the magnetic solitons with a period-like external potential that converts its transmission mode to a controlled oscillation.

Resonant dynamics of three-dimensional skyrmionic textures in thin film multilayers

Skyrmions are topological magnetic solitons that exhibit a rich variety of dynamics, such as breathing and gyration, which can involve collective behavior in arrangements like skyrmion lattices. However, such localized excitations typically lie in the gap of the spin wave spectrum and do not couple to propagating modes. By combining magnetic force microscopy, broadband ferromagnetic resonance, and micromagnetics simulations, we show that in thin-film multilayers of [Pt/FeCoB/AlOx]20 a high-frequency (>12 GHz) mode accompanies the skyrmion lattice phase, which involves the coherent precession of the skyrmion cores that results in the generation of 50–80 nm wavelength spin waves flowing into the uniformly magnetized background. This observation is made possible by a Gilbert damping constant of ∼0.02, which is nearly an order of magnitude lower than in similar ultrathin materials. The simulations also reveal a complex three-dimensional spin structure of the skyrmion cores, which plays a key role for spin wave generation.

Emergent Magnetic Field and Nonzero Gyrovector of the Toroidal Magnetic Hopfion

Magnetic hopfions are localized magnetic solitons with a nonzero 3D topological charge (Hopf index). Herein, an analytical calculation of the magnetic hopfion gyrovector is presented and it is shown that it does not vanish even in an infinite sample. The calculation method is based on the concept of the emergent magnetic field. The particular case of the simplest nontrivial toroidal hopfion with the Hopf index in the cylindrical magnetic dot is considered and dependencies of the gyrovector components on the dot sizes are calculated. Nonzero hopfion gyrovector is important in any description of the hopfion dynamics within the collective coordinate Thiele's approach.

Particle-continuum duality of skyrmions

Topological solitons are crucial to many branches of physics, such as models of fundamental particles in quantum field theory, information carriers in nonlinear optics, and elementary entities in quantum and classical computations. Chiral magnetic materials are a fertile ground for studying solitons. In the past a few years, a huge number of all kinds of topologically protected localized magnetic solitons have been found. The number is so large, and a proper organization and classification is necessary for their future developments. Here we show that many topological magnetic solitons can be understood from the duality of particle and elastic continuum-medium nature of skyrmions. In contrast to the common belief that a skyrmion is an elementary particle that is indivisible, skyrmions behave like both particle and continuum media that can be tore apart to bury other objects, reminiscing particle-wave duality in quantum mechanics. Skyrmions, like indivisible particles, can be building blocks for cascade skyrmion bags and target skyrmions. They can also act as bags and glues to hold one or more skyrmions together. The principles and rules for stable composite skyrmions are explained and presented, revealing their rich and interesting physics.

Nucleation and collapse of magnetic topological solitons in external magnetic field

Nucleation and collapse of magnetic topological solitons in external magnetic field

Crossover of critical behavior and nontrivial magnetism in the chiral soliton lattice host Cr1/3TaS2

The chiral magnetic soliton, a topological kinklike spin texture, has significant applications in spintronic components. In this work, a crossover of critical behavior is found in ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$, a chiral magnetic soliton host with the highest ${T}_{C}$ to date. Angular-dependent magnetization reveals that ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$ exhibits an easy orientation within the isotropic $ab$ plane, but displays anisotropy with the $c$ axis. By using a modified iterative method, two distinct sets of critical exponents, including ${\ensuremath{\beta}}_{\ensuremath{-}}=0.3190(1)$ and ${\ensuremath{\gamma}}_{\ensuremath{-}}=1.263(8)$ for $T\ensuremath{\le}{T}_{C}$, and ${\ensuremath{\beta}}_{+}=0.3475(2)$ and ${\ensuremath{\gamma}}_{+}=1.385(5)$ for $T\ensuremath{\ge}{T}_{C}$, are acquired on both sides of the transition. Analysis of the exponents indicates a crossover of the magnetic interaction from a three-dimensional Ising type below ${T}_{C}$ to a three-dimensional Heisenberg type above ${T}_{C}$, implying nontrivial magnetism in this system. Based on universality scaling, a detailed $H\ensuremath{-}T$ phase diagram around ${T}_{C}$ is constructed for $H\ensuremath{\perp}c$. The crossover of the critical behavior in ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$ is peculiar to chiral magnetic soliton hosts, suggesting that the three-dimensional magnetic coupling is replaced by a one-dimensional one in the chiral magnetic soliton phase via a phase transition.

Crystal field excitation in the chiral helimagnet YbNi3Al9

A crystal field level scheme of a uniaxial chiral helimagnet $\mathrm{Yb}{\mathrm{Ni}}_{3}{\mathrm{Al}}_{9}$, exhibiting a chiral magnetic soliton lattice state by Cu substitution for Ni, has been determined by inelastic neutron scattering. The ground and the first excited doublets are separated by 44 K and are simply expressed as $\ensuremath{\alpha}|\ifmmode\pm\else\textpm\fi{}7/2\ensuremath{\rangle}+\ensuremath{\beta}|\ensuremath{\mp}5/2\ensuremath{\rangle}$, with $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ nearly equal to $\ifmmode\pm\else\textpm\fi{}1/\sqrt{2}$. The easy axis of the crystal field anisotropy is the $c$ axis when the excited levels are populated at high temperatures and high magnetic fields. On the other hand, the magnetism at low temperatures and low magnetic fields, where only the ground doublet is populated, is described by an easy-plane anisotropy which may be treated as an $S=1/2$ system with an anisotropic $g$ factor, ${g}_{xy}=3.02$ and ${g}_{z}=1.14$. An orbital-dependent exchange interaction is also discussed to explain the temperature dependence of the magnetic susceptibility based on this level scheme.

Transformation from Magnetic Soliton to Skyrmion in a Monoaxial Chiral Magnet.

Topological spin textures are of great interest for both fundamental physics and applications in spintronics. The Dzyaloshinskii-Moriya interaction underpins the formation of single-twisted magnetic solitons or multi-twisted magnetic skyrmions in magnetic materials with different crystallographic symmetries. However, topological transitions between these two kinds of topological objects have not been verified experimentally. Here, the direct observation of transformations from a chiral soliton lattice (CSL) to magnetic skyrmions in a nanostripe of the monoaxial chiral magnet CrNb3 S6 using Lorentz transmission electron microscopy is reported. In the presence of an external magnetic field, helical spin structures first transform into CSLs and then evolve into isolated elongated magnetic skyrmions. The detailed spin textures of the elongated magnetic skyrmions are resolved using off-axis electron holography and are shown to comprise two merons, which enclose their ends and have unit total topological charge. Magnetic dipolar interactions are shown to play a key role in the magnetic soliton-skyrmion transformation, which depends sensitively on nanostripe width. The findings here, which are consistent with micromagnetic simulations, enrich the family of topological magnetic states and their transitions and promise to further stimulate the exploration of their emergent electromagnetic properties.

Driving a magnetic texture by magnon currents

Thermally induced spin dynamics in solids have sparked broad interest in both fundamental physics and spintronic applications. As theoretically proposed, thermally excited magnons created by temperature gradients can be used to manipulate spin textures such as topological magnetic solitons. However, so far, the effectiveness of such thermomagnonic torques remained a problem in practice. Here, the dynamics of magnetic vortex cores in thin ferromagnetic platelets driven by thermomagnonic torques are investigated using high-resolution Lorentz transmission electron microscopy. Large deflections of the magnetic vortex core transverse to the direction of the temperature gradient are observed. A generalized Thiele equation model is used to identify the magnitude of the contribution of the involved torques. Our results pave the way for the manipulation of magnetic domains on the nanoscale by thermomagnonic currents and provide insights into the interplay of temperature and spin.

Soliton locking phenomenon in bulk single crystal of monoaxial chiral magnet MnNb3S6

MnNb3S6 is a monoaxial chiral magnet and stabilizes magnetic solitons in the presence of a magnetic field (H). The number of solitons can be controlled by varying H. Furthermore, MnNb3S6 exhibits magnetization relaxation due to soliton annihilation, that is, a nonequilibrium chiral soliton lattice (CSL) state. In this study, we observed soliton locking phenomena in a CSL state on bulk MnNb3S6 crystal, as on micro-processed crystals of CrNb3S6. Thus, we could create nonequilibrium and equilibrium CSL states and switch between them. A numerical simulation revealed that the soliton number was preserved in the soliton locking region; thus, magnetization relaxation was not observed.

Magnetic solitons due to interfacial chiral interactions

We study solitons in a zig-zag lattice of magnetic dipoles. The lattice comprises two sublattices of parallel chains with magnetic dipoles at their vertices. Due to orthogonal easy planes of rotation for dipoles belonging to different sublattices, the total dipolar energy of this system is separable into a sum of symmetric and chiral long-ranged interactions between the magnets where the last takes the form of Dzyaloshinskii–Moriya (DM) coupling. For a specific range of values of the offset between sublattices, the dipoles realize an equilibrium magnetic state in the lattice plane, consisting of one chain settled in an antiferromagnetic (AF) parallel configuration and the other in a collinear ferromagnetic fashion. If the offset grows beyond this value, the internal DM field stabilizes two Bloch domain walls at the edges of the AF chain. The dynamics of these solitons is studied by deriving the long-wavelength lagrangian density for the easy axis antiferromagnet. We find that the chiral couplings between sublattices give rise to an effective magnetic field that stabilizes the solitons in the antiferromagnet. When the chains displace respect to each other, an emergent Lorentz force accelerates the domain walls along the lattice.